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D₇×D₅⋊M₁₆ #72218304

order	2240
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

D₇×D₅⋊M₁₆

Splittings

Hall	C₅×C₇ ⋊ C₂²×M₁₆
Sylow	C₇ ⋊ C₂×D₅⋊M₁₆
Sylow	C₅ ⋊ C₂×D₇×M₁₆

Subgroups

	subgroup	G/H
center	C₄	C₂×D₇×AGL(1,𝔽₅)
commutator, socle	C₂×C₅×C₇	C₂³×C₄
Frattini	C₂	C₂²×D₇×AGL(1,𝔽₅)
Fitting	C₂×C₄×C₅×C₇	C₂×C₄
prime radical	C₂²×D₅×D₇	C₄
cosocle	C₇×Dic₅	C₂⁴
hypercenter	C₂×C₄	D₇×AGL(1,𝔽₅)
hypocenter	C₅×C₇	C₂²×M₁₆
LCS	G ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄

596 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₇)×D₅⋊M₁₆, D₇×M₁₆×AGL(1,𝔽₅), D₇×#65767, …
maximal normal subgroup of	AGL(1,𝔽₇)×D₅⋊M₁₆, D₇×M₁₆×AGL(1,𝔽₅), D₇×#65767, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.